The present invention relates to a spectacle lens designing method and a spectacle lens designed by the same.
The Listing""s Law in an eyeball motion means that, when an eyeball looks far forward (first eye position), a rotation axis of the eyeball motion exists in a surface including the center of rotation of the eyeball and being perpendicular to this eye position (Listing""s surface). In this case, when the eyeball rotates from the first eye position along spectacle principal meridians (representing two vertical and horizontal lines orthogonal to each other on a Gaussian curved surface and representing the same below) according to the Listing""s Law at the time one wears astigmatic spectacles, the spectacle principal meridians and axes of a coordinate system rotating according to the Listing""s Law become parallel to each other and an angle between them becomes 0.
However, when the eyeball motion changes in a direction different from the spectacle meridians, the angle made by the spectacle meridians and the coordinate axes rotating according to the Listing""s Law do not become 0 to cause an angle deviation.
By taking this angle deviation of the coordinate system into consideration, an accurate astigmatism and curvature of field (also called a power error) can be calculated.
A spectacle lens designing method in which this eyeball motion (Listing""s Law) is taken into consideration is disclosed in Japanese Patent Laid-open No. Sho 57-10112 (hereinafter, referred to as Prior art 1)(refer to FIG. 5 in Prior art 1).
Meanwhile, optimization of evaluation functions for several kinds of aberrations, a lens shape, and so on by optimization calculation in an aberration correction process in designing a lens is known as is disclosed, for example, in Japanese Patent Publication No. Hei 2-38930.
To explain the outline of this optimization calculation, taking designing of a single vision aspherical lens for example, though it is a known technique in spectacle lens designing, data on a lens material and prescription specifications are given as basic design specifications, items such as a center thickness are further included as additional specifications in a case of a positive lens, and a combination of refractive surface shapes of a front surface and a rear surface which satisfies them and has as small an optical aberration as possible is obtained by calculation. The refractive surface is expressed as a surface which is mathematized by a function and the function consists of a plurality of parameters defining a spectacle lens. The parameters include a refractive index of the material, a lens diameter, radii of curvature of the front surface and the rear surface, the center thickness, an aspherical conic coefficient, a high degree aspherical coefficient, and so on. They are classified into fixed factors and variable factors according to the object of the lens designing, and the variable factors are dealt as variable parameters.
Then, using a ray tracing method and a wave front tracing method, a plurality of evaluation points whose distances from an optical axis on the refractive surface are different are set on the lens surface, the optical aberration on each of the evaluation points is expressed as an evaluation function (merit function), and calculation to obtain the minimum evaluation function is done using an optimization calculation method such as a damped least square method. At this time, simulations are repeated while operating the variable parameters of the refractive surface, and when a target value is obtained, the final shape of the refractive surface is determined.
As the parameters constituting the evaluation function (merit function) in the optimization calculation, an astigmatism and a curvature of field are generally known, and in a case, for example, when the front surface and the rear surface are both spherically designed in a designing method in a prior art, assuming that the aberrations showing, in a unit of diopter, two focal positions Ft, Fs obtained by the ray tracing method based on a focus D obtained by a paraxial ray tracing are t (tangential error) and s (sagittal error) as shown in FIG. 11, a lens in which the astigmatism=(txe2x88x92s) is minimum is called a Tscheming Form and a lens in which the curvature of field=(t+s)/2 is minimum is called a Percival Form. In Japanese Patent Publication No. Sho 42-9416, an evaluation function in which t and s are complicatedly combined and which is expressed as a horizontal aberration is disclosed.
A distortion aberration is known to be also an important evaluation function in the aforesaid design optimization calculation, and designing in which it is taken into consideration is proposed, for example, in Japanese Patent Laid-open No. Sho 55-59425 (hereinafter, referred to as Prior art 2) and APPLIED OPTICS, Vol. 21, No. 162982-2991: written by Milton Katz (hereinafter, referred to as Prior art 3).
As one of free curved surfaces among lens refractive surface shapes, an atoric surface is known besides a spherical surface and an astigmatic surface. The use of a spline function as an equation used to express the atoric surface is disclosed in Japanese Patent Laid-open No. Sho 62-30216 (Prior art 4) and an equation using orthogonal functions of xy is disclosed in International Publication No. WO 93/07525 (hereinafter, referred to as Prior art 5) is disclosed.
In recent years, however, it has been found out that visual acuity is closely related to processing in the brain and it has been known that the visual acuity is mainly constituted by an image on a retina and processing of the image in the retina and the brain.
Meanwhile, in the designing of spectacle lenses in the prior art, such an idea has been dominant that performance of a spectacle lens is improved as optical performance of the lens becomes higher.
For example, in the optimization calculation method described above, the evaluation function in the prior art is based on an evaluation only by optical calculation, such as evaluation of the size of an image and t (tangential error) and s (sagittal error) of the aberration and so on which are calculated at a far point sphere (FPS) in FIG. 11 by the ray tracing method, and furthermore, an image plane or a retina surface are also dealt as a film surface of a camera without considering a physiological function of an eye such as the eyeball motion.
Furthermore, since the distortion aberration is dealt as an optical amount of a camera as described above also in the above-mentioned Prior art 3, the evaluation function used in it is different from an evaluation function based on a visual angle magnification M which is used in spectacles (for example, KOHGAKU (OPTICS), Vol. 19, No. 10 xe2x80x9cFutatabi Kakubairitsu nitsuite (On Angle Magnification Again)xe2x80x9d Kazuo Miyake), and furthermore, an astigmatic lens and the designing in which the eyeball motion is taken into consideration are not disclosed either. Furthermore, the above-mentioned Prior art 2 does not disclose any concrete technical content thereof and its actual state is not clear.
Meanwhile, in lens designing, the use of the spline function for the atoric surface having a higher degree of freedom of expression, which is disclosed in the above-mentioned Prior art 4, enables the expression of free surface shapes, but it has a disadvantage that it basically lacks precision in surface expression. Moreover, in the above-mentioned Prior art 5, the properties of the eyeball motion using the Listing""s Law are not utilized to result in an insufficient optical surface.
Prior art 1 discloses a designing method in which the eyeball motion is taken into consideration using the Listing""s Law. However, here, the explanation of the above-described technical idea is focused on, and in the concrete lens designing, performance evaluation is made based only on an astigmatism derived from optical calculation, and an evaluation function in the optimization calculation is insufficient.
Moreover, no concrete disclosure on the expression of a lens surface is given.
Furthermore, designing in this Prior art 1 is essentially the same as the one in the prior art based on the idea that performance of a spectacle lens is improved as optical performance becomes higher and it gives no consideration to the correlation with visual acuity.
Thus, it is clear that performance evaluation of a spectacle lens based only on indexes such as an optical amount on the retina and the aberrations is inaccurate as a simulation on a living human body since no consideration is given to the viewpoints of the processing in the retina and the brain and of the eyeball motion as described above.
An object of the present invention, which is made to solve these problems, is to provide a spectacle lens with high performance which improves visual acuity and to provide a designing method of the same.
In order to solve the above-described problems, a first invention is
a spectacle lens designing method in which an eyeball motion (Listing""s Law) is taken into consideration, and which is characterized in that a merit function used in optimization calculation processing of lens designing includes a visual acuity evaluation function (logMAR) derived from a visual acuity measured value V,
where the visual acuity evaluation function (logMAR) is expressed by the following equation (1), letting a curvature of field be an aberration of a spectacle lens and a residual astigmatism be an astigmatism defined from spectacle lens designing in which the Listing""s Law is taken into consideration:
the visual acuity evaluation function (logMAR)=log10 (1/V (curvature of field, residual astigmatism))xe2x80x83xe2x80x83(1)
A second invention is a spectacle lens designing method which is characterized in that, in the spectacle lens designing method of the first invention, letting the visual acuity measured value V be V=2xe2x88x92xxc2x7K (where K={(residual S diopter+residual C diopter/2)2+ (residual C diopter/2)2}1/2 and X is a coefficient between 0.5 and 2 according to actual measurement data), the visual acuity evaluation function (logMAR) is expressed by the following equation (2) which is an approximate equation:
the visual acuity evaluation function (logMAR)=Xxc3x97log102xc3x97{curvature of field2+(residual astigmatism/2)2}1/2xe2x80x83xe2x80x83(2)
A third invention is a spectacle lens designing method which is characterized in that, in the spectacle lens designing method of the first invention, the merit function includes an evaluation function on a distortion aberration (residual distortion aberration DIST) and the evaluation function is expressed by the following equation (3):
residual distortion aberration DIST=Signxc3x97100xc3x97(absolute value of residual visual angle magnification/absolute value of central visual angle magnification M0) xe2x80x83xe2x80x83(3)
where:
the residual visual angle magnification is the distortion aberration defined from the spectacle lens designing in which the Listing""s Law is taken into consideration; and
Sign is a positive/negative sign.
A fourth invention is a spectacle lens designing method which is characterized in that, in the lens designing method according to any one of the first invention to the third invention, the merit function is used in optimization calculation of lens designing of a bi-aspherical lens in which a front surface is an axially symmetrical aspherical surface and a rear surface is an aspherical surface expressed by the following equation (4):                     Z2        =                              c            ⁡                          (              θ              )                                ·                                    r              2                        /                          (                              1                +                                                                            1                      -                                                                        (                                                      1                            +                                                          k                              ⁡                                                              (                                θ                                )                                                                                                              )                                                ·                                                                              c                            ⁡                                                          (                              θ                              )                                                                                2                                                ·                                                  r                          2                                                                                      )                                                  +                                                      ∑                    n                                    ⁢                                                            a                      ⁡                                              (                                                  n                          ,                          θ                                                )                                                              ·                                          r                      n                                                                                                                              (        4        )            
where:
c(xcex8), k(xcex8) are functions for an azimuth xcex8;
a(n, xcex8) is a function for an n degree of a distance r and the azimuth xcex8;
as for a definition domain of the azimuth xcex8, 0 degree to 90 degrees represents 0 degree to 360 degrees due to plane symmetry of an astigmatic lens;
c(xcex8) is a curvature of a lens center and is expressed by the following equation (5) based on the Euler""s theorem, letting a curvature of a spectacle principal meridian in the Gaussian curve theorem be c(0) at 0 degree and c(90) at 90 degrees. In this case, 0 degree is a spherical diopter axis and 90 degrees is a cylinder diopter axis;
c(xcex8)=c(0)xc2x7cos2xcex8+c(90)xc2x7sin2xcex8xe2x80x83xe2x80x83(5)
k(xcex8), which is similar to c(xcex8) above, represents an equation in which the sign c is replaced by the sign k in the above equation (5); and
a(n, xcex8) satisfies requirements of plane continuity and plane symmetry, is a surface further satisfying a requirement of a surface which is capable of controlling an aberration due to an angle deviation which occurs due to the Listing""s Law, and further satisfies the following conditions {circle around (1)} to {circle around (4)}:
{circle around (1)}: having a functional relation of the azimuth xcex8 from 0 degree to 90 degrees;
{circle around (2)}: a linear differential coefficient of the azimuth xcex8 is 0 from 0 degree to 90 degrees;
{circle around (3)}: a high degree differential coefficient is continuous; and
{circle around (4)}: having a control parameter group Ps(n) which is capable of controlling a value of a(n, xcex8) at an angle xcex8 of a function between the azimuths 0 degree and 90 degrees (where 1 to 3 are preferable for s, and n signifies a degree in the above equation (4)).
A fifth invention is a spectacle lens designing method which is characterized in that, in the spectacle lens designing method according to the fourth invention, a(n, xcex8) in the above equation (4) is expressed by the following equation (6) which is a quartic polynominal of the azimuth xcex8, letting a be a(n, 0), a(n, 45), and a(n, 90) when the azimuth xcex8 is 0 degree, 45 degrees, and 90 degrees respectively:
a(n, xcex8)=a(n, 0)+(xe2x88x9211 
xc2x7a(n, 0)+16 
xc2x7a(n, 45)xe2x88x925 
xc2x7a(n, 90)) 
xc2x7xcex82/(4xc2x7902)+(9 
xc2x7a(n, 0)xe2x88x9216 
xc2x7a(n, 45)+7xc2x7a(n, 90)) 
xc2x7xcex83/(4xc2x7903)+(xe2x88x922 
xc2x7a(n, 0)+4xc2x7a(n, 45)xe2x88x922 
xc2x7a(n, 90)xc2x7xcex84/(4 
xc2x7904)xe2x80x83xe2x80x83(6)
where a control parameter is one for the degree n of the distance r from the center and a control parameter P1(n) is a(n, 45).
A sixth invention is a spectacle lens designing method which is characterized in that, in the spectacle lens designing method according to the fourth invention, a(n, xcex8) in the above equation (4) is expressed by the following equation (7), letting a be a(n, 0) and a(n, 90) when the azimuth xcex8 is 0 degree and 90 degrees respectively:
a(n, xcex8)=a(n, 0)xc2x7cos2xcex8+a(n, 90)xc2x7sin2xcex8+P1(n)xc2x7sin2(2xc2x7xcex8)xe2x80x83xe2x80x83(7)
where a control parameter is one control parameter P1(n) for the degree n of the distance r from the center.
A seventh invention is a spectacle lens which is characterized in that it is designed by the spectacle lens designing method according to any one of the first invention to the sixth invention.